Instructor: Michelle R. Greene, Ph.D

Email: mgreene2@bates.edu

Office hours: TTh 8-9am, 4-6pm (Hathorn 106) If neither of these times work, please know that I’m happy to meet when my door is open!

Logistics: T/Th 9:30pm - 10:50 (P’Gill 312) T or Th 1:00-4:00 (Hathorn 207)

Prerequisites: NS/PY 160 or 200 PSYC 218 or any 200-level mathematics course

Course Description

In this course, students will examine formal models of brain function to determine how neurons give rise to thought. Examining real datasets, students will explore how the brain encodes and represents information at cellular, network, and systems scales, and discuss ideas about why the brain is organized as it is. Specific topics include spike statistics, reverse correlation and linear models of encoding, dimensionality reduction, cortical oscillations, neural networks, and algorithms for learning and memory. All assignments, and most class work emphasizes computer programming in Matlab (though no background is assumed or expected).

Introduction

“All models are wrong, but some models are useful” - George Box
“The world you perceive is a drastically simplified model of the world” - Herb Simon

How does the brain work? You’ve been taking neuroscience courses for a couple of years now - do you feel like you have an answer? What does it even mean to say that you understand the workings of the brain? This course takes an epistemological stance based on computation. In other words, our standard for understanding the brain is this: if you can express a neural process in mathematics, and if those expressions fit real-world data, then we understand this process. This is a rigorous definition, and as you will see in this course, it is a standard that we are still striving to achieve in most corners of neuroscience. This presents us with a tremendous intellectual opportunity: there are many ways to make a fundamental contribution to neuroscience, and we have more resources at our disposal now than ever!

The goal of this course is to give you experience in implementing significant models in neuroscience that span several levels of analysis, ranging from the single neuron to the level of the whole organism. Some of these models are historically important, such as the Nobel Prize-winning model of the action potential from Hodgkin and Huxley. Others involve using state-of-the-art machine learning in order to gain insight into brain imaging. As a consequence of this course, you will have the methods at your disposal to analyze real data in just about any neuroscience lab you enter.

As a side effect of this process, you will learn the basics of scientific computer programming. Programming is the literacy of the 21st century. As computers play a larger role in our lives, a gulf has emerged between those who use computer programs and those who write computer programs. As computer programming has obviated many professions and stands on the cusp of killing more, programming skills are a great way to future-proof your life, no matter what your post-Bates plans might be.

I won’t lie - this is not an easy course. You will likely be introduced to new mathematical concepts. You will be wearing many different hats as we shift levels of analysis from physics, through chemistry, biology, psychology, logic, computer science, and even philosophy. If you are new to computer programming, you will be learning an entirely new language by immersing yourself in it. The word choice here is intentional: success in this course will require frequent and deep engagement with difficult problems. However, I can also promise you that your perseverance will be richly rewarded with a new, deeper view of the neuroscience landscape, new frameworks for thinking, and new tools at your disposal.

Learning Objectives:

By the end of the course, you should be able to:

  • Think computationally about neuroscience problems at several levels of analysis. This means clearly articulating the problem at hand with well-defined inputs and outputs, applying appropriate quantitative reasoning to the journey between input to output, and quantitatively evaluating the quality of your model.

  • Apply knowledge of the fundamentals of computer programming by manipulating, analyzing, and visualizing real-world datasets.

  • Conceptually articulate the underlying mathematics of these models. This means being able to describe foundational concepts in linear algebra, differential equations, and probability theory such as vector spaces, eigenvectors and eigenvalues, numerical methods for integration, conditional probability, and Bayes’ theorem; and be able to use these concepts in implementing models of neural activity.

  • Describe several critical levels of analysis where one can model neural function. Compare and contrast among the different levels and evaluate the utility of each level for explaining how we perceive, think, and remember.

Classroom Expectations:

Commitment to Diversity

I expect all students to be respectful of the widely varied experiences and backgrounds represented by the classroom members as a group. Disrespect or discrimination on any basis will not be tolerated. Whether inside or outside the classroom, if you encounter sexual harassment, sexual violence, or discrimination based on race, color, religion, age, national origin, ancestry, sex, sexual orientation, gender identity/expression, or disability, you are encouraged to report it to Gwen Lexow, Director of Title IX and Civil Rights Compliance at Bates at glexow@bates.edu or 207-786-6445. Additionally, please remember that Bates faculty are concerned about your well-being and development, and we are available to discuss any concerns you have. Students should be aware that faculty are legally obligated to share disclosures of sexual violence, sexual harassment, relationship violence, and stalking with the college’s Title IX Officer to help ensure that your safety and welfare are being addressed.

Academic Integrity

Please remind yourself of the Bates College policy on academic integrity. Please read this guide and its definitions of plagiarism, use/misuse of sources, and cheating. Students’ work will be closely scrutinized for plagiarism and violations of the College policy will not be tolerated. If you are concerned that your collaboration might put you at risk of an academic integrity violation, please come see me during office hours as soon as possible.

Students with Learning Differences

If you have a condition or disability that creates difficulties with the assignments, please notify me as soon as possible. You will need to create documentation with the Office of the Dean of Students, so if you need accommodation, please do this as soon as possible.

The math issue

In my experience, few things fill students with existential angst more than mathematics. I have structured this course to be appropriate to those with a variety of formal backgrounds, and it is therefore more conceptual than mathematical. I want you to understand and be able to explain what the various techniques and models do, not necessarily conduct mathematical proofs that demonstrate how they work. A full understanding of many of our class topics would require background in linear algebra, differential equations, probability, and physics. However, I do not expect you to have this background and I will present what you need to know from these topics on a “just in time” basis. However, this is designed to allow you to understand what the mathematical concepts represent, not necessarily to be able to do the math yourself. Of course, I welcome you to go further if you have the background and/or inclination to do so. The most important thing to remember is: ask lots of questions! I am more than willing to repeat anything that is difficult or to explain it from another direction.

Grading:

Concept quizes: 30% total
The beginning and end of each class will be devoted to a short concept quiz. The quiz at the beginning of class will test your familiarity with the content presented in the readings, and the quiz at the end of class will allow you to place class content within the knowledge framework that we will build over the course of the semester. For example, in week N you may be asked to list the advantages that a technique from that week’s readings has over a technique learned in week N-3. These will be graded on a 0-3 scale as follows: 0: Absent; 1: Major errors; 2: Good (modal grade); 3: Exceptionally good answer. (You should consider 3 to be extra credit). Your lowest two grades will be dropped, and no make up is available for quizzes.
 

Problem sets: 25% total
Distributed equally on four problem sets introduced in lab. Problem sets allow you to take a deeper dive into the techniques, give you practice in analyzing real neural data, and in some cases replicate Nobel Prize-winning work! Although not all labs have a problem set, other labs will introduce concepts and techniques that you will need to be successful in your problem set, and attendance is mandatory. Each problem set will be due one week after the lab in which it was introduced.   Hodgkin & Huxley Model: Due week of October 9
Receptive Field Mapping: Due week of October 30 Perceptron: Due week of November 13 Decoding: Due week of December 4   Your written work on the problem set will count for 70% of this grade. The remaining 30% comes from code walks. For each problem set, you will schedule a 15-minute meeting with me where we will discuss your approach to the problem set. This serves two purposes: first, it enforces fair collaboration between students, and more importantly, it allows me to give you credit for correct thinking that doesn’t necessarily lead to successful implementation.
 

Final project: 25% total
The final project for this course will be a formal conference-style paper. Your paper will focus on analysis of real neural data using one or more of the techniques learned in class. You can obtain data from a Bates lab if you are involved in research, or from a number of government or open science initiatives. Your paper is limited to 8 pages in NIPS format (single spaced, double column). There is no minimum length, but you will need to fully describe your problem, review current approaches to the problem, and articulate the details of your approach in reference to the previous literature in addition to showing your results and conclusions. You may have additional pages that contain only your cited references. During our last class session, we will have a symposium in which you will present a short “lightning talk” that showcases the main findings of your project. Following each talk, we will have a few minutes for discussion and questions. You will grade your colleagues and be graded both on the quality of your presentation as well as the quality of your contributions during the Q&A sessions.

  • Topic proposal due to me in Week 8 (with possible required rewrite) (5%)
  • Lightning talk on the last day of class (5%)
  • Written paper (10%)
  • Peer grade on presentation and feedback (5%)

 

Coding Challenges: 10% total
Because computer programming is learning a language, the more you immerse yourself in this language, the more you will be able to do. Programming only once a week in lab will not be sufficient. To kickstart the process, the first eight weeks of class will feature three coding challenges a week that will keep you thinking in the language of code. These will be due Monday, Wednesday, and Friday of each week at 23:59 and will be graded in a Pass/No Pass binary manner.

Participation: 10% total
“Computers are useless. They can only give you answers” - Pablo Picasso
“What people think of as the moment of discovery is really the discovery of the question” - Jonas Salk
  Learning is not a spectator event: you need to ask questions. If you are confused about something, odds are good that you are not the only one. Questions also serve a more fundamental role in memory encoding and learning. If you are thinking about questions, you are integrating what you are learning into your existing knowledge structures. Questions often lead to creative scientific thought. This is an active classroom. Come to class ready to work, ask questions, experiment, and help your classmates, and this is 10% of your grade that you will not need to worry about.

Grade Percentage Grade Percentage
A+ >95% B- 71-74%
A 87-94% C+ 67-70%
A- 83-86% C 63-66%
B+ 79-82% D 50-62%
B 75-78% F <50

Final note about grading
No single component listed above is worth more than 10% of your final grade. This is intentional. This allows anyone to bounce back from a less-than-optimal score on any assignment. If you approach this course with consistent effort, you will succeed!  

Reading:

All required papers will be available on this website and Lyceum, and should be done before class.

Policies:

Collaboration:

Collaboration is the basis of all scientific discovery and is often instrumental in the learning process. However, you are individually responsible for learning the course content. I encourage students to form study groups. However, if you are working together on a problem set or final project, then you must give written credit to the collaborators. The final written product must be your own. In other words, you may conceptually discuss the approach with your group, but you must write your code on your own. If you are working in pairs for the final project, you must also attach a statement of contribution to your paper, which does not count towards page count. As there are many valid approaches to coding the same solution, acts of co-coding are easy to identify and will be treated as violations of academic integrity.

Late work:

For all of our deadlines, if you turn in a component late, you will lose 10% of the total score per day. For example, the maximum possible percentage for a product turned in one day late is 90. This policy does not apply to a documented personal or family emergency.

Emergencies:

If I must cancel class due to weather or an emergency, I will inform you via the class email list. Please consider your Bates email to be the default place to look for class-related information and get into the habit of checking it daily.

Electronics:

Please silence your cell phone upon entering class and refrain from using it during class. In general, this is a laptop-free classroom. There are good reasons for this: laptop use is correlated with lower learning outcomes for you and those around you, and the act of taking notes on the laptop is less effective than hand-written notes. There will be exceptions to this rule for various activities, and these will be advertised in advance.

Course Calendar

 

September 6: NO CLASS: MRG AT CONFERENCE  

 

Lab 1: Introduction to Matlab Programming, part 1

September 11: What is computational neuroscience?

  • Read: O’Reilly (n.d.) Introduction. Computational Cognitive Neuroscience Wiki
     

September 13: What is computation?

Lab 2: Introduction to Matlab Programming, part 2

September 18: Meat circuits: how an electrical engineer views the neuron

  • Read: Section 5.2 from Dayan & Abbott Theoretical Neuroscience
     

September 20: Integrate and fire models

  • Read: Section 5.4 from Dayan & Abbott Theoretical Neuroscience
     

Lab 3: Integrate and fire models

September 25: Hodgkin & Huxley model

September 27: Hodgkin & Huxley model, continued

Lab 4: Hodgkin & Huxley Problem Set

October 2: Spike train statistics: quantifying what neurons “say”

October 4: Spike-triggered average: what caused the neuron the fire?

  • Read: Section 1.3 from Dayan & Abbott Theoretical Neuroscience

 

Lab 5: Spike-triggered statistics

October 9: Extending STA: reverse correlation

October 11: Rate codes versus time codes: what is the language of the brain?

No lab this week: fall break

October 16: Hebbian learning: what fires together, wires together

October 18: NO CLASS: FALL BREAK

 

Lab 6: Receptive field mapping and reverse correlation problem set

October 23: Hebbian learning, continued

  • Read: Gerstner (pages 10-14)

  • Read: O’Reilly (section 4.4 through 4.5.1, non-inclusive)
     

October 25: McCulloch & Pitts Neurons: the simplest silicon neuron

Lab 7: Linear algebra bootcamp

October 30: Perceptron learning algorithm

  • Read: Shiffman Neural Networks from The Nature of Code

  • Final Project Proposal Due
     

November 1: Feedforward neural networks and backpropagation

Lab 8: Neural network problem set

November 6: Feedforward neural networks and backpropagation, continued

November 8: Philosophy of classification

Lab 9: Probability bootcamp and introduction to decoding

November 13: Decoding: nuts and bolts

November 15: Case studies in decoding

  • Come to class prepared to discuss a recent decoding paper you have read.  

NO LAB THANKSGIVING WEEK

November 20: NO CLASS: THANKSGIVING BREAK

 

November 22: NO CLASS: THANKSGIVING BREAK

 

Lab 10: Decoding problem set

November 27: Representational Similarity Analysis

November 29: Representational Similarity Analysis, continued

Lab 11: Representational Similarity Analysis

December 4: Synthesis: do we have what we need to understand the brain?

December 6: FINAL PRESENTATIONS

  • Final written product due